The Wildcats moved a half game in front of Oregon for the lead in the Pacific-12 Conference, but needed a late surge to do it.
Stanford held a 54-49 lead with 5:45 to play, then fell to a 24-12 Arizona rush down the stretch.
Lyons made 9-of-13 from the field and was backed up by Solomon Hill, who scored 20 of his 23 points in the second half. Arizona (20-2, 8-2 Pac-12) has won four in a row since falling at home to UCLA.
Stanford had won three straight, including a surprising victory over Oregon. Dwight Powell scored 24 points to lead the Cardinal, who produced the first 10 points of the game.